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Millennium Management·AI Engineer·Technical Phone Screen·Senior

Senior
Jun 2026

Summary

Interviewed for an AI Engineer role at Millennium Management and got hit with a data structures question that felt more like a backend engineering screen than anything ML-related. Not a bad experience, just not what I expected going in.

Questions Asked (1)

Q1

How would you design a system to store a continuous stream of incoming words such that anagrams are grouped together and can be retrieved efficiently? Walk through your data structure choice, time complexity for inserts and lookups, and how you'd handle deletions or a very large vocabulary.

Algorithms & Data StructuresSystem DesignTechnical Trade-offs
Author's notes

I knew the sorted-key trick from grinding leetcode so the basic answer came out fine.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the requirements: continuous stream, grouping anagrams, efficient retrieval, and scalability. Then propose a hash map where the key is a canonical representation of the anagram group (e.g., sorted word or character count signature) and the value is a set of words. Discuss time complexity for inserts and lookups, and address deletions and large vocabulary with strategies like sharding, caching, or probabilistic data structures.

Pro tip: Mention that the choice of canonical key affects performance: sorting is O(k log k) per word, while a character count signature is O(k) but may have collisions; for large alphabets, a prime product hash can be used but risks overflow. Tailor the choice to the expected word length and alphabet size.

1. Clarify Requirements and Assumptions

Ask about the expected volume, latency requirements, and whether deletions are frequent. Clarify if the stream is unbounded and if memory is a constraint.

2. Choose Canonical Representation

Decide on a method to generate a key for each word such that all anagrams map to the same key. Common methods: sorted string, character count array, or prime product.

3. Design Data Structure

Use a hash map from canonical key to a set (or list) of words. For efficient deletions, use a hash set for each group. Consider concurrency for streaming inserts.

4. Analyze Time and Space Complexity

Insert: O(k) or O(k log k) to compute key, plus O(1) average for hash map insertion. Lookup: O(1) average to find group, O(1) to check membership. Space: O(N * k) for N words of length k.

5. Address Scalability and Deletions

For large vocabulary, shard the hash map by key, use a distributed cache, or employ a trie for prefix-based retrieval. For deletions, remove from the set and delete the key if the set becomes empty. Consider using a count-min sketch for approximate membership if memory is tight.

Key Points to Mention

  • Canonical key generation: sorted string vs. character count vs. prime product, with trade-offs.
  • Hash map with chaining or open addressing for collision resolution.
  • Time complexity: O(k) or O(k log k) for key generation, O(1) average for insert/lookup.
  • Handling deletions: remove from set, clean up empty keys, and consider tombstones in distributed settings.
  • Scalability: sharding, consistent hashing, distributed cache (e.g., Redis), or using a trie for prefix queries.
  • Memory optimization: use of compact representations, compression, or probabilistic data structures for very large vocabularies.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.